Vernon Smith:An Experimental Study of Competitive

Market Behavior

Thanks to David Cooper @ Florida State for sharing his notes

Agenda

Overview of supply & demand in an experiment• These notes summarize, other notes on web site

give more details

Vernon Smith’s classic paper

Key Features of a Double Auction

Both sellers and buyers call out prices• Buyers “bid” and sellers “ask”

Trading takes place during a trading period

A trade take place when • a buyer accepts a sellers ask• a seller accepts a buyers bid

Buyers

each buyer has a “marginal benefit” table for the good

gain or reward is the difference between marginal benefit and the price • try to get a low price, but compete with other

buyers

Any new bid must be higher than outstanding bid

Sellers

each seller has a “marginal cost” schedule for the good

seller’s gain or reward is the difference between the price and the marginal cost• try to get a high price, but must compete with

other sellers

Any new ask must be lower than outstanding ask

07_01 THE MODEL TO EXPLAIN ITTHE MARKET INTERACTION

QUANTITY DEMANDED

Market demand

26 buyers (consumers)

A

ZN

LB

GX R

M

Q

TK

C

I

D ES

J

WV

UF P

A HY

O

Y H IB

BJ

Y

F

E

SC

G

Z

QP L

D

R

H

VUO

K

T

N

M

XI

WA

AL

M DU

N

CZ

OP

V B

S W Q

G X YH R

FT E

K J

I

U

G SZ

EO

PXD

LJ

R

V

T

F

C

KQ W

N

M

PRICE

QUANTITY SUPPLIED

Model of Firm Behavior

Competitive Equilibrium Model

Model of Consumer Behavior

QUANTITY

Market supply

Market supply

PRICE

Market demand

PRICE

26 sellers (firms)

Market: Interaction of 26 consumers and 26 firms

07_03A

$25

20

15

10

5

Buyer A

Items MB1 2 3 4 5

25 20 15 10 5

$25

20

15

10

5

Buyer B

Items MB1 2 3 4 5

24 19 14 9 4

$25

20

15

10

5

Buyer C

Items MB1 2 3 4 5

23 18 13 8 3

$25

20

15

10

5

Buyer D

Items MB1 2 3 4 5

22 17 12 7 2

1 2 3 4 50 1 2 3 4 50 1 2 3 4 50 1 2 3 4 50 1 2 3 4 50

$25

20

15

10

5

Buyer E

Items MB1 2 3 4 5

21 16 11 6 1

Individual Demand Curves

07_03B PRICE

QUANTITY5 10 15 20 25

$25

20

15

10

5

0

07_01 THE MODEL TO EXPLAIN ITTHE MARKET INTERACTION

QUANTITY DEMANDED

Market demand

26 buyers (consumers)

A

ZN

LB

GX R

M

Q

TK

C

I

D ES

J

WV

UF P

A HY

O

Y H IB

BJ

Y

F

E

SC

G

Z

QP L

D

R

H

VUO

K

T

N

M

XI

WA

AL

M DU

N

CZ

OP

V B

S W Q

G X YH R

FT E

K J

I

U

G SZ

EO

PXD

LJ

R

V

T

F

C

KQ W

N

M

PRICE

QUANTITY SUPPLIED

Model of Firm Behavior

Competitive Equilibrium Model

Model of Consumer Behavior

QUANTITY

Market supply

Market supply

PRICE

Market demand

PRICE

26 sellers (firms)

Market: Interaction of 26 consumers and 26 firms

05_A

This is 2 meters high.

No, it's 50 meters high.

Demand curve

Price2 meters

10

20

30

40

50

Dupuit's Vision of Consumer Surplus

07_2A

Q

$2.00

1.00

Ken buys 4.

P

1 2 3 4 5 6

$2.00

1.00

P

1 2 3 4 5 6

$2.00

1.00

0Q

Maria buys 4.

P

1 2 3 4 5 6

$2.00

1.00

1.80

.80

1.60

.60

1.40

.40

1.20

.20

0

DD

Q

Hugo produces 5.

P

1 2 3 4 5 6

$2.00

1.00

0

Q

Mimi produces 3.

P

1 2 3 4 5 6

$2.00

1.00

0

S

S

07_04A

1 2 3 4 50

$25

20

15

10

5

Seller A

Items MC1 2 3 4 5

5 10 15 20 25

1 2 3 4 50

$25

20

15

10

5

1 2 3 4 50

$25

20

15

10

5

1 2 3 4 50

$25

20

15

10

5

1 2 3 4 50

$25

20

15

10

5

Seller B

Items MC1 2 3 4 5

4 9

141924

Seller C

Items MC1 2 3 4 5

3 8

13 18 23

Seller D

Items MC1 2 3 4 5

2 7

12 17 22

Seller E

Items MC1 2 3 4 5

1 6

11 16 21

Individual Supply Curves

07_04B PRICE

QUANTITY5 10 15 20 25

$25

20

15

10

5

0

07_05 PRICE

QUANTITY5 10 15 20 25

$25

20

15

10

5

0

Market supply curve

Market demand curve

Assumptions of Perfect Competition

Agents are rational and selfish utility or profit maximizers

A homogeneous well defined good is traded

There are numerous firms and consumers

Agents are price takers

All these assumptions can frequently be questioned• In many instances people are boundedly rational• People often have interdependent utility functions• There are many markets with only a few firms • In most markets there is no auctioneer but agents set prices.

Chamberlin‘s Experiment

Chamberlin (1948) conducted a market experiment in which prices and quantitites failed to converge to the competitive equilibrium.

• Subjects bargained bilaterally.• Trading prices were written on the blackboard.

Chamberlin’s aim was to refute the competitive model.

V. Smith‘s ExperimentVernon Smith introduced two changes relative to Chamberlin’s trading institution: • (Oral) double auction instead of bilateral bargaining.• Stationary replication, i.e., there were several trading periods

with the same supply and demand structure.• There should be a chance that the market equilibrates over

time.“These two changes seemed to me the appropriate modifications to do a more credible job of rejecting competitive price theory, which after all, was for teaching, not believing (everyone at Harvard knew that, and you just knew, deep down, that those Chicago guys also knew it).” (Smith 1991, p. 155)

How to Win a Nobel Prize in 3 Easy Steps . . .

Some papers are important as much for what they started as for what they are. Smith’s 1962 paper on markets is an archetypical example of this. It wasn’t the first paper ever written in experimental economics. Thurstone had written an influential experimental paper on indifference curves in 1933 and Chamberlin, Smith’s advisor, wrote an important experimental paper on markets in 1948. However, these papers were largely isolated events. After Smith’s work, experimental economics became an ongoing line of research within economics.

“Columbus is viewed as the discoverer of America, even though every school child knows that the Americas were inhabited when he arrived, and that he was not even the first to have made a round trip, having been preceded by Vikings and perhaps others. What is important about Columbus’ discovery of America is not that it was the first, but that it was the last. After Columbus, America was never lost again.” – Al Roth

Christopher Columbus

Research Question

Smith’s experiments were designed to study the neo-classical theory of competitive markets. This is the simple model of supply and demand curves that every economics student learns in the first few lecture of principles. In spite of the importance of the competitive model to economics, there was little direct evidence prior to Smith’s work that the theory actually would work. • Field data is too dynamic to see if equilibrium is being achieved.• Chamberlin’s (1948) earlier work using a decentralized market mechanism found

that generally the prices were too low and the volumes too high as compared to competitive equilibrium predictions.

• Smith’s experiments were designed to give the theory its best chance to work – this reflects a desire to establish if there were any cases where the market would equilibrate as predicted by the theory.

Smith was interested in studying what configurations of supply and demand were most (or least) likely to lead to equilibrium, and was also interested in the dynamics that led to equilibrium

Experimental Design and Procedures

Sessions were run in classrooms for hypothetical payoffs. • The results were later replicated using monetary payoffs. • In one session the subjects were graduate students in a class on economic

theory.• In evaluating Smith’s work, it is important to remember that he was first.

Subjects were divided into two groups, buyers and sellers. • To induce demand and supply curves, each buyer was given a card with

his/her maximum willingness to pay and each seller was given a card with his/her minimum reservation price.

• Each subject was allowed to buy/sell one unit of the good per trading period.

• Trading takes place through a double oral auction. Unlike Chamberlin’s earlier work, this is a highly centralized market. Buyers and sellers are aware of all bid, asks, and transaction prices.• Also multiple rounds• Varied supply and demand conditions

Summary of Sessions

The sessions focus primarily on the effect of vary the shape of the supply and demand curves. Some attention is also paid to the effect of changing market institutions and making traders more experienced..• Test 1: Basic supply and demand• Tests 2 and 3: Varies steepness of supply and demand curves without changing equilibrium

price. This allows Smith to study the process that leads to equilibrium.• Test 4: Flat supply curve. This leaves no surplus for the sellers. • Test 5: Studies the effect of an increase in demand. Given that subjects don’t know how

demand has changed, you might expect this to disrupt convergence.• Test 6: Equilibrium gives a very large surplus to the sellers by using a supply curve that goes

vertical. • Test 7: Very steep supply curve relative to the demand curve.• Test 8: Buyers were not allowed to make bids in early periods. This was supposed to simulate

retail markets. The question is whether this prevents convergence to equilibrium.• Test 9 and 10: Each individual is allowed to make two transactions, doubling the amount of

experience received. This is expected to speed convergence.

What is the prediction?

“The mere fact that ... supply and demand schedules exist in the background of a market does not guarantee that any meaningful relationship exists between those schedules and what is observed in the market they are presumed to represent. All the supply and demand schedules can do is set broad limits on the behaviour of the market. ... In fact, these schedules are modified as trading takes place. Whenever a buyer and a seller make a contract and “drop out” of the market, the demand and supply schedules are shifted to the left in a manner depending on the buyer’s and seller’s position on the schedules. Hence the supply and demand functions continually alter as the trading process occurs. It is difficult to imagine a real market process which does not exhibit this characteristic.” (Smith 1991, p. 12)Nothing ensures that trade will take place at the CE. Notice that the number of CE-trades is in general smaller than the number of economically feasible trades. In principle it might be possible that all feasible trades take place (see Chart 1, Smith 1962). There exists no rigorous theory about behaviour in the DA (though see Sadrieh 2000).

Hypothesis

“Prices converge to the CE”• define: a = standard deviation of trading prices in a

period relative to the CE-price. • a decreases over time.

“Trading efficiency is high”• Efficiency = sum of realized incomes/maximal

aggregate income

21

Symmetric Supply and Demand Functionsprices converge ( declines)

22

Market responds quickly to changes in equilibrium prices

Results – Convergence to Equilibrium

The double oral auctions tend to converge strongly towards equilibrium and achieve high levels of efficiency. For example, the results for Test 1 are shown top right. This is true even when either demand or supply shifts over time. See Test 5 results, bottom right. This is a very basic result, but is the most important result in the paper. Competitive market equilibrium is a central concept in economic theory, but generally can’t be observed in the field. These results prove that competitive equilibrium can work (but not that it must work).

It can’t be true!

“I am still recovering from the shock of the experimental results. The outcome was unbelievably consistent with competitive price theory. ... But the result can’t be believed, I thought. It must be an accident, so I will take another class and do a new experiment with different supply and demand schedules.” (Smith 1991, p. 156)

25

Very quick convergence with flat demand & supply schedules

26

Somewhat less quick convergence with steep demand & supply schedules

Results – Speed of Convergence

Comparing Tests 2 and 3, the supply and demand curves are flatter in Test 2 than in Test 3. This means that a small change in prices from the equilibrium leads to larger excess demand (amount demanded – amount supplied) in Test 2 than in Test 3. If the speed of adjustment is related to the size of excess demand, we should see faster adjustment in Test 2. This is exactly what is observed in the data.

Smith finds more support for the excess rent hypothesis than for the Walrasian hypothesis. This result is largely of historical interest – the convergence results above are the important results.

Results – Uneven Splits of Surplus

Test 4 and Test 7 both feature uneven (predicted) splits of the total surplus between buyers and sellers. These sessions are among the worst in terms of convergence to equilibrium. • Test 4 prices were consistently above

equilibrium, giving some surplus to the sellers.

• Test 7, which isn’t quite as extreme as Test 4, only converges very slowly to equilibrium. Prices are consistently too low (compared to competitive equilibrium) giving some surplus to buyers.

Results – Inceasing Subjects’ Experience

Tests 9A and 10 replicate Test 7, but allow traders to use their values/costs twice in each period. • By doubling subjects’ experience,

the speed of convergence will be increased.

• This appears to be true, especially if you look at Test 10.

This probably isn’t the right way to test this hypothesis though – what you really want is subjects who have already been in one market experiment to participate in a second experiment with different demand and supply curves.

Conclusions

While Smith draws many conclusions from the data, the most important conclusion is the most basic one: “The most striking general characteristic of tests 1–3, 5–7, 9, and 10 is the remarkably strong tendency for exchange prices to approach the predicted equilibrium for each of these markets.”It must be remembered that Smith designed his experiments to give the theory its best chance. These experiments don’t establish that in general the theory of competitive equilibrium will have much predictive power.On a more general level, this paper played an important role in illustrating how controlled laboratory experiments let economists understand phenomena and theories that were hard to observe in the field. In the field, one never knows what the underlying supply and demand curves are, so you can never truly know that the competitive equilibrium has been achieved. In the lab, you can directly observe the emergence of equilibrium.

Further Research on Markets

Smith’s general results on convergence have been replicated many times. DOA markets are remarkably good at converging to equilibrium under a wide variety of circumstances. This remains true even if supply and demand curves are shifting (although random shifts do worsen convergence).

Convergence can be quite sensitive to market institutions. Seemingly small changes in the rules for queuing can substantially affect the speed of convergence. Larger changes in the institutions such as using a posted price market can greatly slow convergence, even leading to non-convergence in some cases.

Market power has mixed effects on convergence to equilibrium. Holt, Langan, and Villamil (1986) find prices that are significantly above equilibrium when sellers have market power, but others have found little effect in DOA markets. More generally, the impact of market power is going to depend on the game being played. When a single individual can easily manipulate market prices or when institutions reduce competition among sellers, departures from equilibrium are more likely. Game theory does a fairly good job of predicting when departures from equilibrium are likely, although it does a poor job of predicting the size of these departures.

Summing Up

“In 1960 I wrote up my results and thought that the obvious place to send it was the Journal of Political Economy. It’s surely a natural for those Chicago guys, I thought. What have I shown? I have shown that with remarkably little learning strict privacy a modest number of traders inexperienced tradersconverge rapidly to a competitive equilibrium under the double auction institution mechanism. The market works under much weaker conditions than had traditionally been thought to be necessary. You didn’t have to have large numbers. Economic agents do not have to have perfect knowledge of supply and demand.You do not need price-taking behaviour - everyone in the double auction is a price maker as much as a price taker.A great discovery, right? Not quite, as it turned out. At Chicago they already knew that markets work. Who needs evidence?” (Smith, 1991, p. 157)

POSTED OFFER MARKETS

Posted offer experiments

Posted price = “take-it-or-leave-it”• Essence is similar to ultimatum game

• What are some key differences?

Example of posted offer markets• Retail sales

Why posted prices?• Retail stores have many sales clerks

• Need pricing consistency.• Government regulation

• Shipping industries must often file rates with govt agency• Lack of simultaneity

• Buyers not all in Wal-Mart at the same time looking for the same stuff.

Posted price markets

Typical experimental results• For posted offer markets, prices tend to start above the

competitive equilibrium and slowly converge• For posted bid markets, prices tend to start below the

competitive equilibrium and slowly converge

Plott and Smith (1978)

Compared • posted bid market (buyers post bids)• vs. one-sided oral bid auctions (buyers make and revise bids,

sellers indicate willingness to purchase)

Results• Buyers benefit when they post bids• Slower convergence in posted bid• Lower efficiency in posted bid• Posted bid responds slowly to shifts in supply and demand

The ability to post prices on a take-it-or-leave-it basis provides an advantage to traders on the side of the market who post the prices.

Institutions matter

The sorting out of relationships between trading institutions and market performance is one of the most important contributions of experimental economics.• Most of the following slides taken from Davis

and Holt paper on the web “Markets with posted prices: Recent results from the laboratory”

Posted prices vs. Oral DA: information available

DA: more information available• Flexible, two-sided price negotiations

• Both buyers and sellers see the sequence of bids and asks until a trade is made

• Buyers and sellers can refine their offers

PO: economizes on information• One-sided price posting• Rigid price negotiations

• Sellers must commit to price before having any info revealed

• Sellers cannot observe excess demand

Oral DA vs Posted offer: Typical results

Price convergence• PO markets converge to competitive equilibrium predictions more

slowly and less completely than DA• PO prices tend to converge from above

Oral DA Posted offer

Oral DA vs Posted offer: Typical results

Supply and demand shocks• PO responds slowly to supply and demand shocks• DA responds almost immediately

Oral DA vs Posted offer: Demand shocks

Experimental design– Supply held constant– Periods 1-8

Demand increases by $0.20/unit for all units

– Periods 9-15Demand decreases by

$0.20/unit for all units– Compare Oral DA and

Posted offer

Oral DA vs Posted offer: Demand shocks

PO efficiency: ~48%, DA efficiency: ~98%

Oral DA vs Posted offer:More typical results

Market power• Monopolists able to exercise market power much more effectively

under PO than comparable DA

Explicit collusion (allow sellers to talk)• In theory, collusion or price-fixing is difficult to maintain –

incentives to defect from agreements• Conspiracies not as effective in DA

• Tendency to shade prices during trading action• Conspiracies are often effective in PO

Collusion and Discounts• In markets for major purchases, sellers can often offer private

discounts from “list” prices• Opportunities to offer secret discounts to specific buyer can break

down price-fixing conspiracies

Oral DA vs Posted offer:More typical results

Search costs• Buyers usually incur search or shopping costs

• Driving from Wal-Mart to Target• Theory – could lead to monopoly pricing since no buyer would

want to “shop” unless new price quote is expected to be lower than shopping costs

• Results – shopping costs do raise prices, but not to monopoly levels as predicted.